杨开,重庆大学

Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions between two breathers, as well as between the breathers and solitons. We also find that breathers are as common as solitons, and thus, the breathers in the mKdV and Gardner equations can be considered as a special case. Numerical results also suggest the asymptotic stability for these breathers, which is only proved for the mKdV case, using the cubic nonlinearity. In general, we show that given a generic data, solutions will evolve into the combination of solitons and breathers, plus some radiation part. This phenomenon can be referred to as the "soliton-breather resolution conjecture". The talk is based on a joint work with Chandler Haight, Svetlana Roudenko and Diana Son.